Question

Question 6
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distance covered are straight lines). If the house is situated at (2,4), bank at(5,8), school at (13,14) and office at (13,26) and coordinates are in km.

Answer 1

We know that, distance between two points $(x_1,y_1)$ and $(x_2,y_2)$
$d=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
Now, distance between house and bank
$=\sqrt{(5-2{)}^2+(8-4{)}^2}$
$=\sqrt{(3{)}^2+(4{)}^2}=\sqrt{9+16}=\sqrt{25}=5$
Distance between bank and daughter’s school
$=\sqrt{(13-5{)}^2+(14-8{)}^2}=\sqrt{(8{)}^2+(6{)}^2}=\sqrt{64+36}=\sqrt{100}=10$
Distance between daughter’s school and office = $\sqrt{(13-13{)}^2+(26-14{)}^2}=\sqrt{0+(12{)}^2}=12$
Total distance travelled = 5 + 10 + 12 = 27 units
Distance between house to office = $\sqrt{(13-2{)}^2+(26-4{)}^2}=\sqrt{(11{)}^2+(22{)}^2}=\sqrt{121+484}=\sqrt{605}=24.59\approx 24.6km$
So, extra distance travelled by Ayush in reaching his office =Total distance travelled - Distance between house to office
27 - 24.6 = 2.4km
Hence, the required extra distance travelled by Ayush is 2.4 km.